Laundry treating appliances, such as washing machines, refreshers, and non-aqueous systems, can have a configuration based on a rotating container that defines a treating chamber in which laundry items are placed for treating. In a vertical axis washing machine, the container is in the form of a perforated basket located within a tub; both the basket and tub typically have an upper opening at their respective upper ends. In a horizontal axis washing machine, the container is in the form of a perforated drum located within a tub; both the drum and tub typically have an opening at their respective front facing ends. The laundry treating appliance can have a controller that implements the cycles of operation having one or more operating parameters. The controller can control a motor to rotate the container according to one of the cycles of operation. Considering that sensors add cost to a product, any method that can provide equivalent or better performance without using sensors can enable a cost reduction without negatively impacting capability (and potentially improving capability). Parameter estimation can be used to monitor and optimize the cycles of operation.